Duality is now a well established tool in economic theory. Blackorby, Primont and Russell [1978] and Diewert [1974] survey duality between direct and indirect aggregator functions, cost functions, transformation functions and profit functions. One advantage of the application of duality theory in economic optimization problems is that, by judicious choice of the parent function, the required response functions of an economic agent can be derived without recourse to explicit optimization. This advantage has generally been demonstrated in the context of static optimization problems. However, it seems clear that duality theory would be even more useful in dynamic optimization problems where there should be a greater payoff in avoiding complex explicit optimization. In the context of a dynamic optimization problem, duality relationships between instantaneous functions (such as the parent functions previously referred to) might be termed atemporal duality. Of perhaps more interest, however, would be temporal duality, or the relationship between the present values of sequences of the corresponding instantaneous parent functions. In principle, temporal duality results already exist, since the dualities surveyed in Blackorby, Primont and Russell, for example, are not limited to the context of static optimization. However, in the context of dynamic optimization there remains the problem of linking properties of instantaneous functions with the corresponding temporal, or present value, functions. This link, or intertemporal duality, is the subject of the present paper. Intertemporal duality is examined here in the context of consumer theory. The major theoretical results concern the duality between the instantaneous indirect utility function and the total indirect utility function (hereafter, the optimal value function), on the one hand, and the duality between the instantaneous cost function and the total cost function (hereafter, the wealth function), on the other hand. We provide dynamic analogues of Roy's Theorem and Hotelling's Theorem, which provide a derivation (almost everywhere) of Marshallian and Hicksian demand functions, by simple differentiation of the optimal value function and the wealth function, respectively.